1/(12×13)+1/(13×14)+……+1/(19×20)的值为:A.1/12 B.1/20 C.1/30 D.1/40一道公考题,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 06:21:29

1/(12×13)+1/(13×14)+……+1/(19×20)的值为:A.1/12 B.1/20 C.1/30 D.1/40一道公考题,
1/(12×13)+1/(13×14)+……+1/(19×20)的值为:
A.1/12 B.1/20 C.1/30 D.1/40
一道公考题,

1/(12×13)+1/(13×14)+……+1/(19×20)的值为:A.1/12 B.1/20 C.1/30 D.1/40一道公考题,
1/(12×13)+1/(13×14)+……+1/(19×20)
=(1/12-1/13)+(1/13-1/14)+……+(1/19-1/20)
=1/12-1/20
=2/60
=1/30
选C

c
1/12-1/20=1/30
1/(12*13)=1/12-1/13,消去中间向即可

因为:1/(12×13)=1/12-1/13 1/(13×14)=1/13-1/14。。。。。。。1/(19×20)=1/19-1/20
也就是原式=1/12-1/13+1/13-1/14+1/14-1/15+1/15-1/16+1/16-1/17+1/17-1/18+1/18-1/19+1/19-1/20=1/12-1/20=1/30
所以答案为C